Thermal waves in irradiated protoplanetary disks

Protoplanetary disks are mainly heated by radiation from the central star. Since the incident stellar flux at any radius is sensitive to the disk structure near that location, destabilizing feedback may be present. Previous investigations have shown that the disk will be stable to finite-amplitude temperature perturbations if the vertical height of the optical surface is everywhere directly proportional to the gas scale height and if the intercepted fraction of stellar radiation is determined from the local grazing angle. We show that these assumptions may not be generally applicable. Instead, we calculate the quasi-static thermal evolution of irradiated disks by directly integrating the global optical depth to determine the optical surface and the total emitting area filling factor of surface dust. We show that in disks with modest mass accretion rates, thermal waves are spontaneously and continually excited in the outer disk, propagate inward through the planet-forming domains, and dissipate at small radii where viscous dissipation is dominant. This state is quasi-periodic over several thermal timescales, and its pattern does not depend on the details of the opacity law. The viscous dissipation resulting from higher mass accretion stabilizes this instability such that an approximately steady state is realized throughout the disk. In passive protostellar disks, especially transitional disks, these waves induce significant episodic changes in spectral energy distributions, on timescales of years to decades, because the midplane temperatures can vary by a factor of 2 between the exposed and shadowed regions. The transitory peaks and troughs in the potential vorticity distribution may also lead to baroclinic instability and excite turbulence in the planet-forming regions.